I've had a similar problem with my FE, but without the motordrive. It happens with the higher speeds, 1/500 and above, and on auto. The shutter stays open until the speed is changed to 1/250 or below. There was a recent thread about this which may give some help. I think it came down to part of the mechanism needing cleaned. Mine fixed itself with repeated firing of the shutter. It had been out of use for a while. If it only occurs with the motor fitted, it may be a different issue. I hope you get it fixed. The FE2 is a great camera.
Alex.